Given that E(X) _______, X is considered an unbiased estimator of the population mean?
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Answer: D. u
Explanation
An estimator is statistically unbiased if its expected value precisely equals the true population parameter value. The Greek letter mu represents the population mean parameter in standard statistical notation conventions. Therefore, setting the expected value of the sample statistic equal to u satisfies unbiasedness criteria. Statistical inference relies heavily on sample estimators to approximate unknown parameters of larger underlying populations. Unbiasedness ensures that repeated sampling will neither systematically overestimate nor underestimate the true population parameter. Sampling distributions describe how sample statistics vary across many random samples drawn from a population.
Quality control engineers use unbiased sample means to monitor manufacturing processes without systematic measurement bias. Polling organizations rely on unbiased estimators to project election outcomes accurately from limited survey samples. Selecting unbiased estimators guarantees that statistical conclusions remain valid and free from systematic distortion. Option A is simply an arbitrary letter that holds no standard meaning in population parameter notation. Option B usually denotes a specific sample observation or random variable rather than a population parameter. Option C employs nonstandard capitalization and lettering that does not conform to established statistical conventions.
- Subject
- Mathematics
- Category
- Statistics
- Topic
- —
- Difficulty
- medium
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